Theorems · Theorem · field theory

Function.Periodic.exists_mem_Ioc

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddCommGroup α] [inst_1 : LinearOrder α]
  [IsOrderedAddMonoid α] [Archimedean α],
  Function.Periodic f c → 0 < c → ∀ (x a : α), ∃ y ∈ Set.Ioc a (a + c), f x = f y

If a function f is Periodic with positive period c, then for all x there exists some y ∈ Ioc a (a + c) such that f x = f y.

Defined in

Mathlib.Algebra.Field.Periodic

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean